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Proof step 164 from proof fsync-pages-overwrite (previous step)

# buf = VFS_PAGE_SIZE, # files1[m4].content[m5] = VFS_PAGE_SIZE, (m4 = m ⊃ mkfile(m0, md, # links(m4, dirs), content[n, buf]);files1[m4]) = mkfile(m1, md0, m3, content0), files1[m] = mkfile(m0, md, # links(m, dirs), content), files0[m] = mkfile(m0, md, # links(m, dirs), content1), pcache[datakey(m, n)] = mkpentry(true, buf), pcache[key] = mkpentry(false, files1[m4].content[m5]), key = datakey(m4, m5), key.data?, n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files1), afs-cons(dirs, files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])]), pcache-cons(pcache1, dirs, files0), m4 ∈ files1, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, key ∈ pcache, m5 ∈ files1[m4].content, ⌊err0⌋ , ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.part]), ∀ pageno. (pageno < n ⊃ (pageno ∈ content ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content ↔ pageno ∈ content1) ∧ content[pageno] = content1[pageno] ), ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty) ⊦ m5 ∈ content0 ∧ files1[m4].content[m5] = content0[m5]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 165:
# files1[m4].content[m5] = VFS_PAGE_SIZE, # buf = VFS_PAGE_SIZE, (m4 = m ⊃ mkfile(m0, md, # links(m, dirs), content[n, buf]);files1[m4]) = mkfile(m1, md0, m3, content0), pcache[datakey(m4, m5)] = mkpentry(false, files1[m4].content[m5]), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, # links(m, dirs), content1), files1[m] = mkfile(m0, md, # links(m, dirs), content), n * VFS_PAGE_SIZE < m2, afs-cons(dirs, files1[m, mkfile(m0, md, # links(m, dirs), content[n, buf])]), afs-cons(dirs, files1), afs-cons(dirs, files0), pcache-cons(pcache1, dirs, files0), m5 ∈ files1[m4].content, datakey(m4, m5) ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, m4 ∈ files1, ⌊err0⌋ , ∀ key. (key ∈ pcache ↔ key ∈ pcache1) ∧ pcache[key].page = pcache1[key].page ∧ (pcache[key].dirty → pcache1[key].dirty), ∀ pageno. (pageno < n ⊃ (pageno ∈ content ↔ pageno ∈ content1 ⊕ mkcontent(m, pcache1)) ∧ content[pageno] = (content1 ⊕ mkcontent(m, pcache1))[pageno] ;(pageno ∈ content ↔ pageno ∈ content1) ∧ content[pageno] = content1[pageno] ), ∀ key0. key0 ∈ pcache → key0.data? ∧ # pcache[key0].page = VFS_PAGE_SIZE ∧ key0.ino ∈ files1 ∧ (¬ pcache[key0].dirty → key0.part ∈ files1[key0.ino].content ∧ pcache[key0].page = files1[key0.ino].content[key0.part]) ⊦ m5 ∈ content0 ∧ files1[m4].content[m5] = content0[m5]

Rule argument

Additional information

Used simplifier rules: ⊦ datakey(m, m0).data?; (s)